The weight an object exerts on a scale varies directly with the mass of an object. If a bowling ball has a mass of 6 kg,the scale reads 54.
a.write an equation for the relationship between weight and mass.
b.If another object has a mass of 8 kg, what would the scale read?
w / m = 54 / 6
6 w = 54 m ... w = 9 m
how tho
a. To write an equation for the relationship between weight and mass, we can use the given information that the weight (W) of an object varies directly with its mass (m).
The equation can be written as:
W = k * m
Where W is the weight of the object, m is the mass of the object, and k is the constant of variation. In this case, we can find the value of k using the given information.
Given that when the mass of the bowling ball is 6 kg, the scale reads 54, we can substitute these values into the equation and solve for k:
54 = k * 6
Now, we can solve for k:
k = 54 / 6
k = 9
Thus, the equation for the relationship between weight and mass is:
W = 9 * m
b. If another object has a mass of 8 kg, we can now use the equation we found in part a to find the weight:
W = 9 * 8
W = 72
Therefore, if another object has a mass of 8 kg, the scale would read 72.
a. To write an equation for the relationship between weight and mass, we need to determine the constant of variation (k) that relates the two variables. In this case, since the weight varies directly with the mass, we can use the formula:
Weight = k * Mass
To find the value of k, we can use the given information. When the mass is 6 kg, the scale reads 54 units. Substituting these values into the equation, we get:
54 = k * 6
To solve for k, we divide both sides of the equation by 6:
k = 54 / 6
k = 9
Therefore, the equation for the relationship between weight and mass is:
Weight = 9 * Mass
b. Now that we have the equation, we can use it to determine what the scale would read when the mass is 8 kg. Substituting the mass value into the equation, we get:
Weight = 9 * 8
Weight = 72
Therefore, if another object has a mass of 8 kg, the scale would read 72.